The number of children in each family on a particular city block is shown in the dot plot: Dot plot with Number of Children Per

Answer:

The distance from the point (0,1,1) to the specified line is zero.

Step-by-step explanation:

Considering the parametric equations of the line,

x=2t, y=5-2t, z=1+t

In order to calculate the distance from (0,1,1), we must remove t from the equations above, such that

whose direction ratios are (l,m,n)=(3,2,-2) and the distance from point (a,b,c)=(0,1,1) is defined as

The distance between the point (0,1,1) and (1) amounts to zero. Therefore, the point (0,1,1) is located on the line (1).

Answer:

  (1/10)∛100 ≈ 0.4642

Step-by-step explanation:

For a cubic shape with volume V, the edge length is defined as...

  s = ∛V

and the surface area is given by...

  A = 6s² = 6V^(2/3)

The area-to-volume ratio is therefore...

  r1 = A/V = 6V^(2/3)/V = 6V^(-1/3)

When the volume V is increased by a factor of 10, the new area-to-volume ratio becomes...

  r2 = 6(10V)^(-1/3)

Consequently, the change factor for the ratio is...

  r2/r1 = (6(10V)^(-1/3))/(6V^(-1/3)) = 10^(-1/3) = (1/10)∛100

The change in surface area per unit volume results in a factor of (∛100)/10.

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Example

For a cube with side length 2, the corresponding volume equals 2³ = 8, with a surface area of 6·2² = 24. The resulting area-to-volume ratio is 24/8 = 3.

The area-to-volume ratio changed by a factor of (0.3∛100)/3 = (∛100)/10, as previously noted.

Answer:

a)

The probability can be determined using the complement rule, with the standard normal distribution, an excel sheet, or a calculator.

b)

This probability can also be calculated using the normal standard distribution, an excel sheet, or a calculator.

c)

For this one, the probability can likewise be derived from the standard normal distribution, excel, or a calculator, with specific adjustments:

Step-by-step explanation:

Previous concepts

Normal distribution refers to a symmetric probability distribution centered around the mean, indicating that occurrences near the mean are more common than those far from it.

The Z-score is a statistic that represents a value's relationship to the average of a set of values, expressed in terms of how many standard deviations it is away from the mean.

Part a

Let X denote the random variable representing the lengths within a population, and for our case, the distribution for X is as follows:

Where and

We seek the probability:

The most effective way to solve this is by leveraging the normal distribution and the corresponding Z-score:

By applying this formula, we can find the probability:

Again, this probability can be obtained either using the complement rule, the standard normal distribution, or a calculator.

Part b

This probability can also be computed using either the normal standard distribution, an excel sheet, or a calculator.

Part c

In this case, the probability can similarly be acquired with the help of the standard normal distribution, an excel sheet, or a calculator, with particular adjustments:

Answer:

Width of the rectangular prism

To determine the volume of the rectangular prism, we utilize the following formula:

v = lwh

Where:

v = volume

l = length

w = width

h = height

Now,

The variables provided in the problem include:

v = 138.24 cubic inches

h =  9.6 inches

l = 3.2 inches

w = ?

By substituting these values into the volume formula, we have:

138.24 = 3.2 * w * 9.6

138.24 = 30.72 * w

w = 138.24/30.72

w = 4.5

⇒ Therefore, the width of the rectangular prism measures 4.5 inches.